Nonlinear Creep Model of Paper and Corrugated Board Materials
Abstract: Models of the nonlinear creep behavior of paper, and of the global buckling , local buckling and creep buckling of corrugated board have been developed. The studies of creep and buckling were limited to climate conditions with constant relative humidity. First the short-term elastic buckling of corrugated board panels was studied. Then an appropriate creep equation, based on the Schapery representation, for liner and fluting materials was developed and implemented in a finite element code to study creep buckling and time to failure of a corrugated board panel axially loaded in compression. Experimental tensile creep-recovery tests of 300 g/m2 kraftliner (used for the facing of corrugated boards) and 150 g/m2 semi-chemical testliner (used for the fluting) at 50, 70 and 90%RH were made by a special designed tensile creep tester. Compression creep-recovery tests at 50%RH was made using a compression creep tester developed at STFI. For the short-term loading case, the experimental global buckling and postbuckling deformation performance of a corrugated board panel was found to be in good agreement with the performance predicted by FE-calculation. The calculated local buckling load was however almost 2.5 times higher than the experimentally observed local buckling load in the panel. This discrepancy between the experimental and calculated local buckling load was most probably due to development of global buckling before local buckling of the panel. For the long-term loading case, the Schapery equation was found to give a good representation of the creep behavior of the facing and fluting material and enabled reasonably accurate predictions of the creep behavior of corrugated board. The Schapery representation for paper was implemented in the finite element codes Ansys and Abaqus. In Ansys, the Schapery representation was described by using stress-strain isochrounes and failure of the material was considered by using a Tsai-Wu failure criterion based on a time independent failure strain in the CD and MD at each layer. This model with isochrounes and a material failure criterion was found to be suitable for calculating failure load for a given time to failure. In the calculations made by the finite element code Abaqus no simplification was made of the Schapery representation and no material failure criterion was used. This model is more accurate than the model with isochrounes stress-strain curves in the sense that the influence of stress redistribution on the creep is considered. The model is therefore suitable to study the creep strains of a corrugated board structure as function of time, both the in-plane strains and pre-failure out-of-plane displacements. The creep buckling analysis was verified by tests. It was found that the experimental out-of-plane displacement of the mid-node of a panel under compression load was in good agreement with the calculated out-of-plane displacement.
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